"Grain" typically means the seeds of cereal grasses, of the family Poaceae. Quinoa is the seed of a plant from family Amaranthaceae; it's not a grass, it's a leafy plant from the same taxonomic group as beets and spinach. This leads to it being referred to as a "pseudocereal grain" if it's called a "grain" at all.
cereal grains (from the Poaceae) actually are both a seed and a fruit. In most grasses the ovary wall (fruit) and the seed are fused together into a structure called a caryopsis. Sometimes the ovary wall is milled off before consumption (often with wheat), sometimes not (corn, oats). Grain is not a well defined term, at least botanically. Soybeans, corn and wheat are all considered grains by some (for example, some departments of the US government).
I'm confused about the refrigeration comment though - I make quinoa all the time and have not had that issue.